The England international is believed to be pining for a move away from the Emirates after being demoted to the Gunners' second choice goalkeeper below Brentford loanee David Raya.
Ramsdale's only Premier League starts since the September international break have come against Raya's parent club, where Arsenal emerged on the winning side despite a few blunders from the 25-year-old.
Mikel Arteta sanctioned a new contract for Ramsdale towards the end of last season, though, and the Spaniard has suggested that he wants to keep the ex-Bournemouth and Sheffield United man at the club for next season.
However, with Ramsdale's spot in future England squads at threat for as long as he sits on the Emirates bench, the shot-stopper is expected to head for the exit door this summer, when Raya's loan from Brentford will be made permanent.
Wolverhampton Wanderers join race for Ramsdale
European giants Chelsea, AC Milan and Bayern Munich have both been tipped to move for the Gunners goalkeeper this summer, while Newcastle United could also throw their hat into the ring.
However, The Sun reports that Wolverhampton Wanderers have now taken an interest in signing Ramsdale, as they prepare for the possibility of Jose Sa's summer exit.
The 31-year-old recently signed a long-term extension at Molineux, which runs until 2027 with the option of a further year, but he is believed to be attracting interest from Saudi Arabia.
Wolves are supposedly prepared to grant Sa's wish for an exit, and head coach Gary O'Neil may drop the Portuguese from the first XI during the closing stages of the season.
Ramsdale is just one of a few goalkeepers under consideration by Molineux chiefs, who are also keeping tabs on Liverpool's Caoimhin Kelleher and Sunderland's Anthony Patterson.
Which goalkeepers could replace Ramsdale at Arsenal?
After facing incessant questions over his controversial goalkeeping decision every time Raya made a slight mistake, Arteta's bold call to drop a man who kept 14 Premier League clean sheets last season has been vindicated.
On course for the Premier League's Golden Glove with 13 clean sheets to his name this season, Raya will be Arsenal's number one for 2024-25 and beyond, forcing the Gunners to try to find a willing second choice.
Sunderland's Patterson has been mooted as a potential target, as have fellow European stoppers Diant Ramaj (Ajax) and Giorgi Mamardashvili (Valencia).
Alternatively, the Gunners could look across the Atlantic for a new second-fiddle goalkeeper and are believed to have been impressed by Athletico Paranaense's Bento, as well as Patrick Schulte of Colombus Crew.